<html>
<head>
<meta http-equiv="content-type" content="text/html; charset=utf-8">
</head>
<body text="#000000" bgcolor="#FFFFFF">
<p>In the NMR filter the <img alt="$\hat{Z}$"
style="vertical-align: middle;"
src="cid:part1.1379077F.F4414259@mercer.edu"> matrix elements
are built from terms that look like</p>
<p><br>
</p>
<p><img alt="$\left(e^{-i2\pi /N}\right)$" style="vertical-align:
middle;" src="cid:part2.42CEC836.D44BBCF4@mercer.edu"></p>
<p>the exponential is Euler's method for expressing a complex number</p>
<p><img alt="$e^{i\theta}=\cos(\theta) + i \sin(\theta)$"
style="vertical-align: middle;"
src="cid:part3.65AAF227.1980BC8F@mercer.edu"></p>
<p>so in thic case <img alt="$\theta=-2\pi/N$"
style="vertical-align: middle;"
src="cid:part4.CA3505BA.8C7377BB@mercer.edu"> and the complex
number could be built in fortran using</p>
<p>cnum = cmplx( cos(2*pi/N), -sin(2*pi/N) )</p>
<p><br>
</p>
<p>and using the GSL and C/C++ it would be something like this</p>
<p>gsl_complex b0 = <span class="pl-c1">gsl_complex_rect</span>(<span
class="pl-c1"></span><span class="pl-c1"></span> cos(2*pi/N),
-sin(2*pi/N) );</p>
<pre class="moz-signature" cols="72">--
Andrew J. Pounds, Ph.D. (<a class="moz-txt-link-abbreviated" href="mailto:pounds_aj@mercer.edu">pounds_aj@mercer.edu</a>)
Professor of Chemistry and Computer Science
Mercer University, Macon, GA 31207 (478) 301-5627
<a class="moz-txt-link-freetext" href="http://faculty.mercer.edu/pounds_aj">http://faculty.mercer.edu/pounds_aj</a>
</pre>
</body>
</html>